On the bound of first excursion probability

Method has been developed to improve the lower bound of the first excursion probability that can apply to the problem with either constant or time-dependent barriers. The method requires knowledge of the joint density function of the random process at two arbitrary instants

Probability of stress-corrosion fracture under random loading

Mathematical formulation is based on cumulative-damage hypothesis and experimentally-determined stress-corrosion characteristics. Under both stationary random loadings, mean value and variance of cumulative damage are obtained. Probability of stress-corrosion fracture is then evaluated, using principle of maximum entropy

Ground State Energy for Fermions in a 1D Harmonic Trap with Delta Function Interaction

Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi method is used as an effective test for the conjecture.Comment: 4 pages, 3 figure

Fatigue crack growth in a particulate TiB2 reinforced powder metallurgy iron-based composite

Fatigue crack growth behavior has been examined in a particulate titanium diboride (TiB2)–reinforced iron-based composite that had been produced via a mechanical alloying process. Comparison with equivalent unreinforced material indicated that fatigue crack growth resistance in the composite was superior to monolithic matrix material in the near-threshold regime. The composite exhibited relatively low crack closure levels at threshold, indicative of a high intrinsic (effective) threshold growth resistance compared to the unreinforced iron. The lower closure levels of the composite were consistent with reduced fracture surface asperity sizes, attributable to the reinforcement particles limiting the effective slip distance for stage I–type facet formation. The observed shielding behavior was rationalized in terms of recent finite-element analysis of crack closure in relation to the size of crack wake asperities and the crack-tip plastic zone. The different intrinsic fatigue thresholds of the composite and unreinforced iron were closely consistent with the influences of stiffness and yield strength on cyclic crack-tip opening displacements. Cracks in the composite were generally seen to avoid direct crack-tip–particle interaction

On deformed double current algebras for simple Lie algebras

We prove the equivalence of two presentations of deformed double current algebras associated to a complex simple Lie algebra, the first one obtained via a degeneration of affine Yangians while the other one naturally appeared in the construction of the elliptic Casimir connection. We also construct a specific central element of these algebras and, in type A, show that they contain a very large center for certain values of their parameters.Comment: 40 page

The nonperturbative closed string tachyon vacuum to high level

We compute the action of closed bosonic string field theory at quartic order with fields up to level ten. After level four, the value of the potential at the minimum starts oscillating around a nonzero negative value, in contrast with the proposition made in [5]. We try a different truncation scheme in which the value of the potential converges faster with the level. By extrapolating these values, we are able to give a rather precise value for the depth of the potential.Comment: 24 pages. v2: typos corrected, clarified extrapolation in scheme B, and added extrapolated tachyon and dilaton vev's at the end of Section